The linear stability of the sheet pinch is examined for a rapidly rotating fluid. The sheet pinch is a horizontal layer of uniform, incompressible, inviscid fluid of densityp, electrical conductivity [sgrave], magnetic permeability μ, confined between two perfectly conducting planesz=0,d, wherezis height. The prevailing magnetic field,B0(z), is horizontal; at each height it is unidirectional, but that direction turns continuously (in one sense only) aszincreases; the system is in magnetostatic equilibrium. The layer rotates about the vertical with an angular velocity, Ω, that is large: Ω>>VA/d, whereVA=B0/√(μp) is the Alfvén velocity and μ is the magnetic permeability. The dimensionless measure of [sgrave] is the Elsasser number A = [sgrave]B02/2Ωp.